In the figure, AQPB and ASRC are squares, and AQS is an equilateral triangle. If QS = 4 and BC = x, what is the value of x? [asy][asy] unitsize(16); pair A,B,C,P,Q,R,T; A=(3.4641016151377544, 2); B=(0, 0); C=(6.928203230275509, 0); P=(-1.9999999999999991, 3.464101615137755); Q=(1.4641016151377544, 5.464101615137754); R=(8.928203230275509, 3.4641016151377544); T=(5.464101615137754, 5.464101615137754); dot(A);dot(B);dot(C);dot(P); dot(Q);dot(R);dot(T); label("$A$", (3.4641016151377544, 2),E); label("$B$", (0, 0),S); label("$C$", (6.928203230275509, 0),S); label("$P$", (-1.9999999999999991, 3.464101615137755), W); label("$Q$", (1.4641016151377544, 5.464101615137754),N); label("$R$", (8.928203230275509, 3.4641016151377544),E); label("$S$", (5.464101615137754, 5.464101615137754),N); draw(B--C--A--B); draw(B--P--Q--A--B); draw(A--C--R--T--A); draw(Q--T--A--Q); label("$x$", (3.4641016151377544, 0), S); label("$4$", (Q+T)/2, N);[/asy][/asy]
Problem
Source:
Tags: ratio
04.11.2012 17:08
I think the answer is 4*3^1/2
05.11.2012 01:56
05.11.2012 10:36
PranayMittal wrote:
I already knew the solution but thanks anyway
06.11.2012 02:00
rachitgoel wrote: PranayMittal wrote:
I already knew the solution but thanks anyway Even if you know the answer, you should still post the solution. It's for other people, not just you.
06.11.2012 13:07
PranayMittal wrote: rachitgoel wrote: PranayMittal wrote:
I already knew the solution but thanks anyway Even if you know the answer, you should still post the solution. It's for other people, not just you. Sorry I am new here .thanks for telling me that
09.11.2012 05:10
Diagram: [asy][asy] unitsize(16); pair A,B,C,P,Q,R,T; A=(3.4641016151377544, 2); B=(0, 0); C=(6.928203230275509, 0); P=(-1.9999999999999991, 3.464101615137755); Q=(1.4641016151377544, 5.464101615137754); R=(8.928203230275509, 3.4641016151377544); T=(5.464101615137754, 5.464101615137754); dot(A);dot(B);dot(C);dot(P); dot(Q);dot(R);dot(T); label("$A$", (3.4641016151377544, 2),E); label("$B$", (0, 0),S); label("$C$", (6.928203230275509, 0),S); label("$P$", (-1.9999999999999991, 3.464101615137755), W); label("$Q$", (1.4641016151377544, 5.464101615137754),N); label("$R$", (8.928203230275509, 3.4641016151377544),E); label("$S$", (5.464101615137754, 5.464101615137754),N); draw(B--C--A--B); draw(B--P--Q--A--B); draw(A--C--R--T--A); draw(Q--T--A--Q); label("$x$", (3.4641016151377544, 0), S); label("$4$", (Q+T)/2, N);[/asy][/asy] The diagram was not in the op there originally, it was added in later. (I did not just copy it for spamming purposes.)
10.11.2012 19:09
Why have you posted the diagram?
10.11.2012 20:10
So it is in the problem thread, and not in a external source.